Null reference models

Drugs produce effects. When drugs are used together (referred to as a drug combination) they can have greater or lesser effects (synergy or antagonism) than when used alone. To distinguish and categorize the combination effect we compare it to the effect that the drugs would have if they were used and no interaction was seen between them (also called the additive effect). A mathematical model that describes the non-interaction between two drugs is called a null reference model (Lederer, Dijkstra, and Heskes 2018). Every null-reference model defines an effect threshold, for which if we observe a greater combination effect we would call the interaction a synergy (an antagonism otherwise). Of course, the distinction does not need to be binary, e.g. the larger the combination effect is from the the additive threshold, the more synergistic the drug combination is (and vise-versa for the antagonism case).

There are two kinds of null reference models: the ones that are effect-based and the ones that are dose-effect based. The distinction is derived from what is used to define the specific thresholds that characterize a synergy effect: just the effects of the combined drugs or also information on their dosages (dose-response curves)? The most common null-reference models in each category are:

  • Effect based
    • HSA (Highest Single Agent)7
    • Bliss Independence (Bliss)
    • Response additivity
  • Dose-effect based
    • Loewe Additivity (Loewe)
    • ZIP Model
    • Explicit Mean Equation Model
    • Others

Effect-based Models

Combination Index (CI)

Dose-Effect based Models

Loewe Additivity

  1. Also known as Gaddum’s non-interaction model↩︎